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Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
0

%I #10 Jul 04 2018 15:31:02

%S 1,23,506,11132,244904,5387888,118533536,2607737792,57370231424,

%T 1262145091328,27767192009216,610878224202752,13439320932460544,

%U 295665060514131968,6504631331310903296,143101889288839872512

%N Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.

%C The initial terms coincide with those of A170742, although the two sequences are eventually different.

%C First disagreement at index 22: a(22) = 356947326335320446369221574403, A170742(22) = 356947326335320446369221574656. - Klaus Brockhaus, Apr 09 2011

%C Computed with MAGMA using commands similar to those used to compute A154638.

%H <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, -231).

%F G.f.: (t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(231*t^22 - 21*t^21 - 21*t^20 - 21*t^19 - 21*t^18 - 21*t^17 - 21*t^16 - 21*t^15 - 21*t^14 - 21*t^13 - 21*t^12 - 21*t^11 - 21*t^10 - 21*t^9 - 21*t^8 - 21*t^7 - 21*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1).

%t coxG[{22,231,-21}] (* The coxG program is at A169452 *) (* _Harvey P. Dale_, Jul 04 2018 *)

%Y Cf. A170742 (G.f.: (1+x)/(1-22*x)).

%K nonn

%O 0,2

%A _John Cannon_ and _N. J. A. Sloane_, Dec 03 2009